Abstract
Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes virus replication and the respective immune response while disease transmission is represented by a simple susceptible-infected (SI) model. The bridge of within- to between-host is by considering transmission as a function of the viral load of the within-host level. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, such as a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. A main result was the derivation of the reproduction number for the between-host as a general increasing function of the reproduction number for the within-host. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.
